论文标题
Leavitt路径代数的简单性通过分级环理论
Simplicity of Leavitt path algebras via graded ring theory
论文作者
论文摘要
假设$ r $是一个关联的Unital环，而$ e =（e^0，e^1，r，s）$是一个有向图。利用分级环理论的结果表明，相关的leavitt路径代数$ l_r（e）$在且仅当$ r $很简单时，$ e^0 $都没有非平凡的遗传和饱和子集，并且$ e $中的每个周期都有退出。我们还对简单的Leavitt路径代数的中心进行了完整的描述。
Suppose that $R$ is an associative unital ring and that $E=(E^0,E^1,r,s)$ is a directed graph. Utilizing results from graded ring theory we show, that the associated Leavitt path algebra $L_R(E)$ is simple if and only if $R$ is simple, $E^0$ has no nontrivial hereditary and saturated subset, and every cycle in $E$ has an exit. We also give a complete description of the center of a simple Leavitt path algebra.
